Party leaders have approached Corker in the past about chairing the NRSC because as a former CEO he has a natural rapport with business leaders who fit the committee’s donor profile. But Corker wants to focus on policy, specifically a grand bargain next year to cut the deficit.

The NRSC chairmanship has been a springboard to the upper ranks of the Senate GOP leadership.

Former Sen. Bill Frist (R-Tenn.) vaulted from the NRSC to Senate majority leader after helping Republicans capture the upper chamber in 2002. McConnell became Senate Republican whip after heading the NRSC in the 1998 and 2000 cycles.

Moran, who was elected to the Senate in 2010 after serving 14 years in the House, has a reputation for being ambitious throughout his congressional career. The freshman has an accomplished record on agriculture issues and sits on the Appropriations Agriculture subcommittee.

A spokeswoman for Moran said her boss is concentrating on helping GOP candidates this fall.

“While he has been encouraged by his colleagues to give the NRSC a serious look, Sen. Moran continues to be focused on making certain Republicans gain a majority in the Senate and win the White House this November,” said Garrette Silverman. “Through his work with FreeState PAC, Sen. Moran is traveling the country to raise money and has given to nearly every Senate candidate this cycle.

“He is also serving as a co-chairman of the Romney Farm and Ranch team,” she added.

One lawmaker cautioned that another contender could emerge because Republicans feel confident they will retake the Senate in 2014 —if not this cycle.

“If Obama wins reelection, and it kind of looks that way now, the president’s party traditionally loses seats in the midterm of the second term. The Democrats have to defend more seats than us. All it’s going to take is a chairman who can walk and chew gum to win back the Senate,” said the source.

Portman could have Senate leadership ambitions since being passed over for Mitt Romney’s running mate. He is one of the biggest fundraisers among the Senate Republican freshman class. A Portman aide did not rule out a bid for NRSC chairman.

“Rob will spend the next month and a half doing everything he can for Romney and [Rep. Paul] Ryan [R-Wis.] in Ohio and to ensure he has as many Republican colleagues as possible with him in the Senate next year. Anything past Election Day will be considered at that point,” said the aide.

Republicans have seen their chances of winning the Senate this year fall since early last year, when they felt assured of seizing the majority. Their prospects took a hit with the surprise retirement of Sen. Olympia Snowe (R-Maine) and Rep. Todd Akin’s (R-Mo.) controversial statement on rape, which spurred the NRSC and Crossroads GPS, a Republican super-PAC, to pull funding from the Missouri race.

“We see John Cornyn in the airport almost every weekend flying to one part of the country or another,” said another lawmaker.

Cornyn has benefited from representing Texas, the wealthiest red state in the nation and home to many super-rich conservative donors he can tap to support GOP candidates. A successor could be hard-pressed to match his fundraising productivity.

Another GOP senator said Moran has a good chance of winning the chairmanship because he is the only person aggressively campaigning for it.